Take a standard 8 \times 8 chessboard and cut off two squares that sit at diagonally opposite corners. Can the remaining 62 squares be covered exactly by 31 dominoes, each covering two squares that share an edge?

A Chessboard with Two Corners Missing

Issue 23 Warm-up Published 5 Oct 2026 By The Chalkboard Desk

The problem

Take a standard chessboard and cut off two squares that sit at diagonally opposite corners. Can the remaining squares be covered exactly by dominoes, each covering two squares that share an edge?

Each domino covers exactly two squares sharing a full side.
Dominoes may not overlap and may not extend beyond the board.

Take a minute

Reveal hint 1

Try it for a while and you will keep failing, but failure is not a proof. Look for a quantity that every domino affects in the same way.

Reveal hint 2

Colour the board like a chessboard. What does one domino always cover?

Solution

AnswerNo. It is impossible.

Derivation

Colour the board.
See what a domino always covers.
Check the effect of removing the corners.
Count what dominoes need.
Conclude.
Note where the argument fails.